Edelweiss Applied Science and Technology ISSN: 2576-8484 Vol. 9, No. 8, 231-253 2025 Publisher: Learning Gate DOI: 10.55214/2576-8484.v9i8.9257 © 2025 by the author; licensee Learning Gate © 2025 by the author; licensee Learning Gate History: Received: 16 May 2025; Revised: 14 June 2025; Accepted: 18 June 2025; Published: 4 August 2025 * Correspondence: hsiang@mail.ntpu.edu.tw Interactions between main Central American and the U.S. stock markets with financial contagion: An application of the FIEC-FIAPGARCH-DCC model Hsiang-Hsi Liu1* 1Graduate Institute of International Business, National Taipei University, New Taipei City 237, Taiwan; hsiang@mail.ntpu.edu.tw (H. H. L.). Abstract: Given the limited empirical evidence on the relationship between the main Central American stock markets (Costa Rica and Panama) and the U.S. stock market, this study aims to empirically examine volatility spillovers, long memory characteristics, asymmetries, and dynamic conditional correlation (DCC) effects among these markets. In addition, we investigate the contagion effects of major financial events across the three stock markets using a multivariate Fractionally Integrated Error Correction (FIEC) model and a Fractionally Integrated Asymmetric Power GARCH (FIAPGARCH) model within DCC framework. Structural breaks associated with the subprime mortgage and Global Financial Crisis (GFC), as well as European Debt Crisis (EDC), are explicitly incorporated into the analysis. Our findings reveal significant cross-market effects, evidence of long-term volatility dependence, and asymmetric volatility responses to positive and negative shocks. Moreover, estimating the power term parameters allows for a nuanced understanding of variance heterogeneity across markets. The observed market interactions stem not only from fundamental co-movement but also from contagion effects triggered by systemic events such as the GFC and EDC. These insights provide valuable implications for financial risk managers, regulators and international investors, offering guidance for portfolio diversification, risk assessment, and strategic asset allocation decisions in an increasingly interconnected global market environment. Keywords: Asymmetric volatility, Contagion effects, FIEC- FIAPGARCH-DCC Model, Long memory, Volatility spillovers. 1. Introduction This study attempts to investigate the interrelationship among Costa Rica and Panama stock markets in Central America with the US stock market and contagion effects of the global financial crises via a multivariate FIEC-FIAPGARCH-DCC models. These empirical models not only measure returns and return volatility spillover, long memory and asymmetric effects among these three stock markets but also distinguish the contagion effect(direct crisis impact) from spillover effect(general market influence). Over the past two decades, financial liberalization and global market integration have heightened interest in cross-border capital flows and diversification. This study examines the interdependence between Central American and US stock markets, particularly during major events like the global financial crisis. As emerging markets attract more investment post-crisis, understanding these linkages is vital for informed portfolio diversification and risk management. Market liberalization has boosted international investment and capital flows, making information transmission key to stock market co- movement. The globalization of finance and faster information spread have heightened the risk of financial crises, as a crisis in one country can quickly spread globally, as seen with the GFC and EDC. https://orcid.org/0000-0001-5363-7505 232 Edelweiss Applied Science and Technology ISSN: 2576-8484 Vol. 9, No. 8: 231-253, 2025 DOI: 10.55214/2576-8484.v9i8.9257 © 2025 by the author; licensee Learning Gate These crises show that stock market integration involves both regional co-movement and contagion from special events. This study focuses on how the GFC and EDC may influence stock returns and volatility in Central America, where trade and investment between Costa Rica, Panama, the U.S., and Europe have grown significantly over the past two decades. The goal is to assess whether these markets are impacted by the contagion effects of these global financial events. Contagion can be studied by observing the increased co-movement during a crisis compared to tranquil periods. In this study, we define contagion as a significant rise in cross-market linkages following a crisis in one country or group of countries. We aim to explore whether contagion affects the stock markets of Costa Rica and Panama. Specifically, we focus on how stock market volatility in developed economies, like the U.S. and Europe, spreads to these Central American markets. Using multivariate co-integration techniques, we analyze the correlation between these emerging markets and U.S. stock prices. Costa Rica and Panama were chosen due to their rapid development, increased market liberalization, and growing financial integration, which have attracted international investors seeking diversification and hedging opportunities. Information shocks drive market volatility, passing return and volatility effects across markets. This study explores information transmission and spillovers in market interactions, including long-memory effects and asymmetric volatility triggered more by negative price changes. Using dynamic conditional correlation (DCC) models, we analyze these effects across the Costa Rican, Panamanian, and US stock markets. Volatility spillovers, long-memory effects, and asymmetries with models like FIAPGARCH- DCC showing how financial data behaves under these phenomena. Previous studies, for example, Aloui [1], Dimitriou, et al. [2], Karanasos, et al. [3], Wajdi, et al. [4], Abed, et al. [5] and Goudarzi, et al. [6] highlight the limitations of GARCH models in explaining long memory and volatility asymmetries. This study moreover focuses on slow-decaying autocorrelation and mean reversion in stock markets, combining the FIAPGARCH-DCC and fractional error correction (FIEC) models [7] to explore market interactions. By integrating these models as FIEC-FIAPGARCH-DCC, we analyze relationships between Central American markets, like Costa Rica and Panama, and the US stock market. The findings offer valuable insights into portfolio diversification and hedging, highlighting Central America’s growing appeal to international investors. The empirical results aim to guide better asset management, allocation, and risk decisions for investors and policymakers. The remainder of this study is structured as follows. In section 2 we detail the methodology framework related to this study. Section 3 presents the empirical results and analyses. While section 4 reports the concluding remarks. 2. Methodology Framework 2.1. Long Memory Properties and Fractionally Integrated Process This study uses a fractionally integrated process to analyze the long-memory behaviors of financial variables. Cheung [8] suggested that if the unit root test’s null hypothesis isn't rejected, the time series is not I (0) stationary, but it may still exhibit long-term, slow mean reversion. Long memory reflects persistent autocorrelation and gradual decay over time [9-13]. It indicates the lasting influence of past periods on the present. In the ARFIMA (p, d, q) model, co-integrated variables are represented by 𝑍𝑡 , and when d=0, it simplifies to a VAR model. For 0 0 and asymmetry coefficient −1 < γi < 1 (for i=1, q). When γi > 0 (<0), negative (positive) shocks give rise to higher volatility than positive (negative) shocks. Under (p = 1, q = 1) the APGARCH (1, 1) models is represented as follow: σt δ = η + α (L)(|εt| − γεt)δ + β (L) σt δ (2) Where α (L)=∑ αi q i=1 , β (L) = ∑ βj p j+1 and L denotes the lag operator The power term coefficient (𝛿) measures the degree of heterogeneous variance, while γ captures the effects of asymmetric shocks. α and β represent the standard ARCH and GARCH parameters, γ is the leverage parameter, and δ is the power term parameter. A positive (negative) γ indicates that negative (positive) past shocks affect current volatility more than positive (negative) shocks. The model applies a Box and Cox [19] transformation to both the conditional standard deviation and asymmetric absolute innovations. In the APGARCH model, good news (εt−1>0) and bad news (εt−1<0) affect future volatility differently, as the conditional variance depends on both the magnitude and sign of εt−1. The FIAPGARCH model combines the long memory properties of the FIGARCH model [20] with the asymmetric power GARCH (APGARCH) model proposed by Ding, et al. [17] to extend the FIGARCH model to account for different degree of heterogeneous variance and asymmetric dynamics [2-5]. Accordingly, the fractionally integrated with APGARCH (1, 1), the FIAPGARCH (1, 1) model can be shown as follows: (1 − βL) σt δ = ω + ((1 − βL) − (1 − αL) (1 − L)d) (|εt| − γεt)δ (3) Alternatively, σt δ = ω + βσt−1 δ + ((1 − βL) − (1 − αL) (1 − L)d)(|εt| − γεt)δ (4) If β = 0 we obtain FIAPARCH (1) as follows: σt δ = ω + (1 − (1 − αL) (1 − L)d)(|εt| − γεt)δ (5) Where L denotes the lag operator, d is the 0 ≤ d ≤ 1 functional differencing parameter, β denotes the autoregressive parameters, α represents the moving average parameters of the conditional variance equation, δ represents the optimal power transformation, γ represents the asymmetry parameter and γ < 1 ensures that positive and negative innovations of the same size can have asymmetric effects on the conditional variance. 2.3. Dynamic Conditional Correlation (DCC)-GARCH Model Engle [21] introduced the Dynamic Conditional Correlation (DCC) model, a multivariate model that can be viewed as a nonlinear combination of univariate GARCH models. The DCC is a generalized version of Bollerslev [22] Constant Conditional Correlation (CCC) model. Utilizing the conditional correlation coefficients and variances of the 𝑖 and 𝑗 stock returns to parameterize the stock return covariance matrix Ht, we specify a multivariate conditional variance: Ht = DtRtDt (6) Where Rt is the (n x n) time-varying correlation matrix; Dt is the (n x n) diagonal matrix of time- varying standard deviations from univariate GARCH models: 234 Edelweiss Applied Science and Technology ISSN: 2576-8484 Vol. 9, No. 8: 231-253, 2025 DOI: 10.55214/2576-8484.v9i8.9257 © 2025 by the author; licensee Learning Gate Dt = diag(h11t 1/2 … h𝑛𝑛t 1/2 ) (7) With hiit 1/2 𝑖th diagonal, 𝑖 = 1,2, . . . , 𝑛; hiit can be any univariate GARCH model The evolution of the correlation in the DCC model is given by: 𝑄𝑡 = (1 − 𝛼 − 𝛽)�̅� + 𝛼𝑢𝑡−1𝑢𝑡−1 ′ + 𝛽𝑄𝑡−1 (8) Where 𝑢𝑖,𝑡 = 𝑖,1 √ℎ𝑖𝑖,𝑡 and 𝑄𝑡 = (𝑞𝑖𝑗,1), the n x n time-varying covariance matrix of is 𝑢𝑡, �̅� = 𝐸[𝑢1𝑢𝑡 ′ ] is the n x n unconditional variance matrix of 𝑢𝑡, and 𝛼 𝑎𝑛𝑑 𝛽 are nonnegative scalar parameters satisfying(𝛼 + 𝛽) < 1. Since 𝑄𝑡 does not generally have ones on the diagonal, we scale it to obtain a proper correlation matrix 𝑅𝑡. Thus, Rt = (𝑑𝑖𝑎𝑔(𝑄𝑡))−1/2𝑄𝑡 = (𝑑𝑖𝑎𝑔(𝑄𝑡))−1/2 (9) Where (𝑑𝑖𝑎𝑔(𝑄𝑡))−1/2 = 𝑑𝑖𝑎𝑔(1/√𝑞11,𝑡, … ,1/√𝑞𝑛𝑛,𝑡) Now Rt is a correlation matrix with ones on the diagonal and off-diagonal elements less than one in absolute value, as long as 𝑄𝑡 is positive definite. A typical element of 𝑄𝑡 is given by: 𝑞𝑖𝑗,𝑡 = (1 − 𝛼 − 𝛽)�̅�𝑖𝑗 + 𝛼𝑢𝑖,𝑡−1𝑢𝑗,𝑡−1 + 𝛽𝑞𝑖𝑗 𝑡−1 (10) Where �̅�𝑖𝑗 is the unconditional correlation of 𝑢𝑖,𝑡 𝑎𝑛𝑑 𝑢𝑗,𝑡. (𝑞𝑖𝑗,𝑡)is the n x n time-varying covariance matrix of 𝑢𝑡, 𝑢𝑖,𝑡−1𝑢𝑗,𝑡−1 is the cross-product of time-varying standardized residuals matrix. α and 𝛽 are non-negative scalars that α + β < 1. Engle [21] defines conditional correlations as a weighted sum of past correlations, modeling 𝑄𝑡 as a GARCH process and transforming it into a correlation matrix. He proposed a two-step estimation procedure for the DCC model. In the first step,the conditional variance Ht = DtRtDt separates volatility and correlation. Replacing Rt with the identity matrix simplifies the likelihood function to a sum of N univariate models’ log-likelihoods. In the second step, Rt parameters are estimated. This method provides consistent but inefficient estimators. The log-likelihood of the two-step procedure can be compared with the one-step method and other models. Now 𝑅𝑡 is a correlation matrix with ones on the diagonal and off-diagonal elements less than one in absolute value, as long as 𝑄12,𝑡 if two markets 1 and 2 is positive definite. A typical element of 𝑅𝑡 is obtained from 𝑄𝑡 of the form as: 𝑞11,𝑡 = (1 − 𝛼 − 𝛽)�̅�11 + 𝛼𝑢1,𝑡−1 2 + 𝛽𝑞11 𝑡−1 (11) 𝑞22,𝑡 = (1 − 𝛼 − 𝛽)�̅�22 + 𝛼𝑢1,𝑡−1 2 + 𝛽𝑞22 𝑡−1 (12) 𝑞12,𝑡 = (1 − 𝛼 − 𝛽)�̅�12 + 𝑎𝑢1,𝑡−1𝑢2,𝑡−1 + 𝛽𝑞12 𝑡−1 (13) Under DCC we can obtain the conditional correlation coefficient for any two markets 1 and 2 as follows: 𝜌12,𝑡 = 𝑞12,𝑡 √𝑞11,𝑡𝑞22,𝑡 = ℎ12,𝑡 √ℎ11,𝑡ℎ22,𝑡 (14) Expressing the correlation coefficient in a bivariate case, we have: 235 Edelweiss Applied Science and Technology ISSN: 2576-8484 Vol. 9, No. 8: 231-253, 2025 DOI: 10.55214/2576-8484.v9i8.9257 © 2025 by the author; licensee Learning Gate 𝜌12,𝑡 = [�̅�12(1−𝑎−𝛽)+𝛼 (𝑢1,𝑡−1𝑢2,𝑡−1)+β(𝑞12,𝑡−1)] √�̅�11 (1−α−β)+α(𝑢1,𝑡−1 2 )+β(𝑞11,𝑡−1) √�̅�22 (1−α−β)+α(𝑢2,𝑡−1 2 )+β(𝑞22,𝑡−1) (15) Based on the (7) equation we derive the conditional covariance equation as follows as equation (9): ℎ12,𝑡 = 𝜌12,𝑡 × √ℎ11,𝑡ℎ22,𝑡 = 𝑞12,𝑡 √𝑞11,𝑡𝑞22,𝑡 × √ℎ11,𝑡ℎ22,𝑡 (16) ℎ12,𝑡 = [�̅�12+𝛼 (𝑢1,𝑡−1𝑢2,𝑡−1−�̅�12)+β(𝑞12,𝑡−1−�̅�12)] √ℎ11,𝑡ℎ22,𝑡 √�̅�11+𝛼 (𝑢1,𝑡−1 2 −�̅�11)+β(𝑞11,𝑡−1−�̅�11) √�̅�22+𝛼 (𝑢2,𝑡−1 2 −�̅�22)+β(𝑞22,𝑡−1−�̅�22) (17) or ℎ12,𝑡 = [�̅�12(1−𝑎−𝛽)+𝛼 (𝑢1,𝑡−1𝑢2,𝑡−1)+β(𝑞12,𝑡−1)] √ℎ11,𝑡ℎ22,𝑡 √�̅�11(1−𝑎−𝛽)+𝛼 (𝑢1,𝑡−1 2 )+β(𝑞11,𝑡−1) √�̅�22(1−𝑎−𝛽)+𝛼 (𝑢2,𝑡−1 2 )+β(𝑞22,𝑡−1) (18) When α+β=0, the model reduces to Bollerslev [22]. The DCC model integrates two GARCH (1,1) processes for stock returns and disturbances. Consequently, the log-likelihood function accounts for stock return fluctuations and correlations. 𝑖(𝜃, 𝜑) = [− 1 2 ∑ (𝑛𝑙𝑜𝑔(2𝜋) + log|𝐷𝑡|2 + 𝑒𝑡 1𝐷𝑡 −2𝑒𝑡)𝑡 ] + [− 1 2 ∑ (log |𝑅𝑡| + 𝑒𝑡 1𝑅𝑡 −1𝑒𝑡)𝑡 ] (19) The first part of the likelihood function represents volatility, as the sum of individual GARCH likelihoods. In the first stage, we maximize the log-likelihood over the parameters in 𝐷𝑡. In the second stage, we estimate correlation coefficients. To obtain more accurate coefficient estimates, we apply the BHHH method to fulfill [23]. 3. Empirical Results and Analysis 3.1. Data and Preliminary Analyses We obtained weekly stock price index data from Bloomberg database for Costa Rica, Panama, and the US (S&P500) from 1st week of January 1994 to 4th week of December 2024. Their respective price indices are Costa Rica Stock Exchange index (CRSMBCT), Panama Stock Exchange Index (BVPS) and one of the United States major Stock Exchange Index (S&P500).The data is expressed as stock returns, calculated as the logarithmic change in closing prices from one week to the next: 𝑅𝑖,𝑡 = (𝑙𝑛𝑃𝑖,𝑡 − 𝑙𝑛𝑃𝑖,𝑡−1) 𝑋 100. Where 𝑅𝑖,𝑡 is the weekly return for stock market i in week t, and 𝑃𝑖,𝑡 and 𝑃𝑖,𝑡−1 are the closing prices for that week and the previous week, respectively. This transformation converts the closing prices into weekly stock price returns. This section provides descriptive statistics for the logarithms of stock prices and stock price returns, including mean, median, maximum, minimum, standard deviation, skewness, kurtosis, Jarque-Bera normality test, and Ljung-Box serial correlation test. An ARCH effect is observed in the statistics for the logarithms and returns of Costa Rica, Panama, and the US, as shown in Table 1. Costa Rica has the highest mean for both the logarithmic stock price (9.1837) and stock return (0.002856), while Panama has the lowest logarithmic mean (4.9718), and the US has the lowest return mean (0.001309). Regarding stock risk, Costa Rica shows the highest standard deviations for both the logarithmic stock price (0.9263) and stock return (0.02223), while the US has the lowest standard deviation for the logarithmic stock price (0.3681), and Panama has the lowest for stock returns (0.01793). The skewness measures 236 Edelweiss Applied Science and Technology ISSN: 2576-8484 Vol. 9, No. 8: 231-253, 2025 DOI: 10.55214/2576-8484.v9i8.9257 © 2025 by the author; licensee Learning Gate indicate that logarithmic stock prices in all three markets are left-skewed (less than 0) and platykurtic less than 3 except for the US which is leptokurtic (3.3447) relative to the normal distribution with logarithm. For stock price returns, the US shows a negative skew (-1.6435), indicating a left-skewed distribution, while Costa Rica (0.8353) and Panama (0.5775) are positively skewed. All stock return variables exhibit leptokurtic distributions, suggesting the presence of fat-tail phenomena. In addition, Jarque-Bera tests reject the normality of stock prices and returns for Costa Rica, Panama, and the US. The Ljung-Box Q-statistic shows autocorrelation in the stock prices and returns for these markets. Significant second-order autocorrelation suggests conditional heteroskedasticity, making the ARCH/GARCH process suitable for modeling their time series behavior. Table 1. Descriptive Statistics of Logarithmic Stock Prices and Stock Price Returns. logarithm of Stock Prices Stock Price Returns Costa Rica Panama US Costa Rica Panama US Mean 10.2175 4.4201 7.2843 0.0031 0.0024 0.0018 Median 9.6104 4.7281 7.1104 0.0008 0.0012 0.0045 Maximum 11.2458 6.0612 7.7821 0.2201 0.1415 0.0915 Minimum 6.8015 2.8011 5.955 -0.1025 -0.1135 -0.2025 Std. Dev. 0.9416 0.8125 0.4105 0.0310 0.0192 0.0205 Skewness -0.9921 -0.4515 -0.7625 0.9102 0.5825 -1.7352 Kurtosis 2.9105 2.4150 3.6152 23.0041 28.1142 20.1150 Jarque-Bera 186.2251*** 54.1102*** 115.3978*** 19201.96*** 11201.28*** 13882.01*** Probability 0.0000 0.0000 0.000000 0.000000 0.000000 0.000000 First-Order Serial Correlation 𝑄(12) 124.25*** 68.910*** 22.152*** 226.75*** 480.76*** 250.26*** 𝑄(18) 141.25*** 83.125*** 32.115*** 252.91*** 515.66*** 261.35*** 𝑄(24) 157.66*** 96.871*** 36.671*** 252.94*** 541.30*** 271.30 *** Second-Order Serial Correlation 𝑄2(12) 241.35*** 492.15*** 268.12*** 440.15*** 801.35*** 531.25*** 𝑄2(18) 261.45*** 515.88*** 274.20*** 460.25*** 826.25*** 526.56*** 𝑄2(24) 262.85*** 538.40*** 283.15*** 465.83*** 866.75*** 554.28*** Note: ***, **, and * denote statistical significance at the 1%, 5% and 10% levels, respectively. The software used by Eviews12. 3.2. Unit Root Tests Table 2 presents the results of unit root tests on the natural logarithms and return series of the weekly indices for Costa Rica, Panama and the US. Both the Augmented Dickey-Fuller (ADF) and Phillips-Perron (PP) tests were applied to the levels and first differences of each series under three regression models: without constant and trend, with constant and trend, and with constant but no trend. The results from both tests reject the null hypothesis of a unit root, indicating that the first differences of each series are stationary. Therefore, all variables are integrated of order one, I(1). 237 Edelweiss Applied Science and Technology ISSN: 2576-8484 Vol. 9, No. 8: 231-253, 2025 DOI: 10.55214/2576-8484.v9i8.9257 © 2025 by the author; licensee Learning Gate Table 2. Results of Unit Root Tests Country With Intercept Term With Intercept and Trend Term Without Intercept and Trend Term Augmented Dickey-Fuller Test Logarithm Costa Rica -4.9101 [4] -4.9951 [4] -4.9101 [4] Stock Price Panama -5.4715[3] -5.4251 [3] -5.6157 [3] Series US -5.2262 [2] -5.3215 [2] -5.1126 [2] Stock Price Costa Rica 13.2811*** [4] 13.4625*** [4] 15.3015*** [4] Return Panama 4.5120*** [3] 4.6254*** [3] 5.1425*** [3] Series US 10.1102*** [2] 9.3781*** [2] 10.2021*** [2] Phillips-Perron Test Logarithm Costa Rica -4.9101 [5] -4.9011 [5] -4.9946 [5] Stock Price Panama -5.4387 [7] -5.4271 [7] -5.3890 [7] Series US -5.0125 [3] -5.0125 [3] -5.1128 [3] Stock Price Costa Rica 14.6231*** [4] 15.6710*** [4] 14.6712*** [4] Return Panama 4.6512*** [6] 4.6266*** [6] 4.6358*** [6] Series US 9.3457*** [2] 9.3578*** [2] 9.3225*** [2] Note: The values in [.] are the most fitting lags determined by the SBC criterion. ***, **, and * denote statistical significance at the 1%, 5% and 10% levels, respectively. 3.3. Testing Results for Structural Breaks To examine how shocks of events influence stock price co-movement or interaction effects in Costa Rica, Panama and the US, the iterated cumulative sums of squares (ICSS) algorithm presented by Incln and Tiao [24] is used to detect variance breaks (volatility shifts) in stock returns. The results suggest that the subprime mortgage crisis and the Global Financial Crisis (GFC) affected the three markets from the 1st week of July 2007 to the 3rd week of April 2009; the European Debt Crisis (EDC) occurred from the 4th week of April 2009 to the 4th week of March 2012; the most intense US-China trade war from the 3rd week of March, 2018 to the 4th week of December 2019 and the COVID-19 pandemic period from the 1st week of March 2020 to the 4th week of December 2020, based on our estimates. 3.4. Johansen Co-integration Tests Based on the unit root test results, it is known that the stock prices of Costa Rica, Panama, and the United States are integrated I(1). When series share the same integration order, a long-term co- integration relationship may exist. To test for this relationship and avoid spurious regression, the Johansen and Juselius [25] method is applied. The Trace and Max-eigenvalue tests identify the number of co-integration vectors, and the parameters are estimated using maximum likelihood. The results, presented in Table 3, show that after taking the natural logarithms of the stock price indices, a long- term co-integrating relationship exists among the three markets. This suggests one statistically significant co-integrating vector in the model, indicating a long-run relationship and co-movement among these three stock markets. 238 Edelweiss Applied Science and Technology ISSN: 2576-8484 Vol. 9, No. 8: 231-253, 2025 DOI: 10.55214/2576-8484.v9i8.9257 © 2025 by the author; licensee Learning Gate Table 3. Johansen Co-integration Tests. Unrestricted Co-integration Rank Test (Trace) Trace Test Hypothesized Trace 0.05 Prob. No. of CE(s) Eigenvalue Statistic Critical Value None 0.0481 72.3588 35.4015 0.0000 At most 1 0.0224 18.4925 21.2271 0.0815 At most 2 0.0060 4.9011 10.9012 0.4125 Unrestricted Co-integration Rank Test (Maximum Eigenvalue) Table 3. Continue… Hypothesized Max-Eigen 0.05 Prob. No. of CE(s) Eigenvalue Statistic Critical Value None 0.0625 54.0012 23.1010 0.000 At most 1 0.0321 14.2121 16.0012 0.1815 At most 2 0.0068 5.0128 10.0254 0.4015 Co-integrating Vector Estimates Panama Costa Rica US C 1 -1.8252*** 1.2021*** 4.6256 -0.2628 -0.7128 -2.8104 Note: ( ) denotes standard deviation. *** show statistically significant at 1% level. According to the results of Table 3, the error correction term 𝑍𝑡−1 can be determined as follows: 𝑍𝑡−1 = 𝑃𝑁𝑡−1-1.8252CR𝑡−1-1.2021US𝑡−1 + 4.6256 (20) Where 𝑃𝑁𝑡−1, CR𝑡−1 and US𝑡−1 are natural logarithms of the stock price index for Panama, Costa Rica and US, respectively. Furthermore, the error correction term (𝑍𝑡) from the co-integration test is used to estimate the autocorrelation function (ACF) shown in Figure 1. The slow decline in autocorrelation coefficient as lags increase suggests that the stock indices require a longer time to achieve co-integration, reflecting long-term memory. Based on fractionally integrated process, the conditional mean equation which contains long memory effects, the co-integration process represented by ( ) ( )  t d LL −−− 11 should be incorporated into the model system, i.e., the fractionally integrated error correction (FIEC) model is considered. Figure 1. 239 Edelweiss Applied Science and Technology ISSN: 2576-8484 Vol. 9, No. 8: 231-253, 2025 DOI: 10.55214/2576-8484.v9i8.9257 © 2025 by the author; licensee Learning Gate ACF of the Error Correction Term 𝑍𝑡 Table 4. Serial Correlation, ARCH and Asymmetric Effect Tests on Standardized Residuals Terms for Estimated FIEC Models. Costa Rica Panama US 𝑍𝐶𝑂𝑅,𝑡 = 휀𝐶𝑂𝑅,𝑡/√𝑣𝑎𝑟 (휀𝐶𝑂𝑅,𝑡) 𝑍𝑃𝐴𝑁,𝑡 = 휀𝑃𝐴𝑁,𝑡/√𝑣𝑎𝑟 (휀𝑃𝐴𝑁,𝑡) 𝑍𝑈𝑆,𝑡 = 휀𝑈𝑆,𝑡/√𝑣𝑎𝑟 (휀𝑈𝑆,𝑡) 𝑄(12) 33.412 33.675 8.210 𝑄(18) 44.295 42.857 16.684 𝑄(24) 49.212 54.625 21.308 𝑍𝐶𝑂𝑅𝑡 2 𝑍𝑃𝑁𝑡 2 𝑍𝑈𝑆𝑡 2 𝑄(12) 269.301*** 215.045** 97.254*** 𝑄(18) 262.045*** 274.695*** 110.254*** 𝑄(24) 261.384*** 326.455*** 128.301*** 𝑍𝐶𝑂𝑅,𝑡 𝑍𝑃𝐴𝑁,𝑡 𝑍𝐶𝑂𝑅,𝑡 𝑍𝑈𝑆,𝑡 𝑍𝑃𝐴𝑁,𝑡 𝑍𝑈𝑆,𝑡 𝑄(12) 91.254*** 25.501*** 48.265*** 𝑄(18) 98.301*** 44.886*** 56.021*** 𝑄(24) 110.246*** 110.200*** 64.245*** Asymmetric Effects Test for FIEC Model Costa Rica Panama US SBT -2.6015*** -0.9925*** 3.6114*** NSBT -3.9124*** -4.4825*** -0.5025*** PSBT 12.1140*** 4.5301*** -0.8015*** JT 162.201*** 45.2301*** 22.001*** Note: 𝑍𝑖,𝑡 = 휀𝑖,𝑡/√𝑣𝑎𝑟 (휀𝑖,𝑡) , 𝑍𝑖𝑡 2 and 𝑍𝑖,𝑡 𝑍𝑗,𝑡 represent standardized residuals, squared standardized residuals and cross-product of standardized residuals, respectively. ** and *** denote statistically significant at 5% and 1% level, respectively. Based on the estimated FIEC model, we calculate the standardized residuals, squared standardized residuals, and their cross-products. The Ljung-Box Q tests (Table 4) show no autocorrelation in the standardized residuals (𝑍𝐶𝑂𝑅,𝑡, 𝑍𝑃𝐴𝑁,𝑡 𝑎𝑛𝑑 𝑍𝑈𝑆,𝑡), but serial correlation exists in the squared residuals (𝑍𝐶𝑂𝑅𝑡 2, 𝑍𝑃𝑁𝑡 2 𝑎𝑛𝑑 𝑍𝑈𝑆𝑡 2) and cross-product of the two standardized residuals (𝑍𝐶𝑂𝑅,𝑡 𝑍𝑃𝐴𝑁,𝑡, 𝑍𝐶𝑂𝑅,𝑡 𝑍𝑈𝑆,𝑡 𝑎𝑛𝑑 𝑍𝑃𝐴𝑁,𝑡 𝑍𝑈𝑆,𝑡), indicating the presences of ARCH effects in the residuals in our model system. The results of testing for asymmetric effects by the sign bias test (SBT), negative sign bias test (NSBT), positive sign bias test (PSBT), and joint test (JT) are statistically significant for the squared standardized residuals, revealing volatility asymmetry in these three stock markets. Consequently, the AP-GARCH model is applied. Moreover, Figure 2 display the autocorrelation function (ACF) of standardized squared residuals, squared standardized residuals, and the cross-product of standardized residuals in the estimated FIEC model for each stock market. The autocorrelation coefficients exhibit slow decay and persistence, indicating long memory properties in return volatilities and co-variances. Some of the researches have proven that the fractionally integrated EC (FIEC) model is empirically important for long-memory in returns, the following results may hold true when modeling long-range dependence in volatility on conditional mean, variance and co-variance equations with dynamic interaction effects, i.e., the FIAPGARCH-DCC model capturing long-memory, asymmetric volatility and DCC effects will also be applying in the model. Thus, the FIEC-FIAPGARCH-DCC is built up for analyzing the interrelationships among these three stock markets. 240 Edelweiss Applied Science and Technology ISSN: 2576-8484 Vol. 9, No. 8: 231-253, 2025 DOI: 10.55214/2576-8484.v9i8.9257 © 2025 by the author; licensee Learning Gate Figure 2. ACF of the First-Power, Squared and Cross Standardized Residuals in the FIEC Model. 241 Edelweiss Applied Science and Technology ISSN: 2576-8484 Vol. 9, No. 8: 231-253, 2025 DOI: 10.55214/2576-8484.v9i8.9257 © 2025 by the author; licensee Learning Gate 3.5. Set-Up of FIEC-FIAPGARCH-DCC Model The FIEC-FIAPGARCH-DCC model of the stock market indexes for Costa Rica, Panama and the US are built up as follows: 3.5.1. Conditional Mean Equations ∆𝐶𝑂𝑅𝑡 = 𝑢1 + 𝜆1[(1 − 𝐿)𝑑 − (1 − 𝐿)]𝑍𝑡 + ∑ 𝑎1𝑖 4 𝑖=1 ∆𝐶𝑂𝑅,𝑡−𝑖 + ∑ 𝑎2𝑖 4 𝑖=1 ∆𝑃𝐴𝑁,𝑡−𝑖 + ∑ 𝑎3𝑖 4 𝑖=1 ∆𝑈𝑆,𝑡−𝑖 + 𝑘1𝐷1 + 𝑘2𝐷2 + 𝑘3𝐷3 + 𝑘4𝐷4 + 휀𝐶𝑂𝑅,𝑡 ∆𝑃𝐴𝑁𝑡 = 𝑢2 + 𝜆2[(1 − 𝐿)𝑑 − (1 − 𝐿)]𝑍𝑡 + ∑ 𝑏1𝑖 4 𝑖=1 ∆𝑃𝐴𝑁,𝑡−𝑖 + ∑ 𝑏2𝑖 4 𝑖=1 ∆𝐶𝑂𝑅,𝑡−𝑖 + ∑ 𝑏3𝑖 4 𝑖=1 ∆𝑈𝑆,𝑡−𝑖 + 𝑘5𝐷1 + 𝑘6𝐷2 + 𝑘7𝐷3 + 𝑘8𝐷4 + 휀𝑃𝐴𝑁,𝑡 ∆𝑈𝑆𝑡 = 𝑢3 + 𝜆3[(1 − 𝐿)𝑑 − (1 − 𝐿)]𝑍𝑡 + ∑ 𝑐1𝑖 4 𝑖=1 ∆𝑈𝑆,𝑡−𝑖 + ∑ 𝑐2𝑖 4 𝑖=1 ∆𝑃𝐴𝑁,𝑡−𝑖 + ∑ 𝑐3𝑖 4 𝑖=1 ∆𝐶𝑂𝑅,𝑡−𝑖 + 𝑘9𝐷1 + 𝑘10𝐷2 + 𝑘11𝐷3 + 𝑘12𝐷4 + 휀𝑈𝑆,𝑡 (21) 3.5.2. Conditional Variance Equations ℎ𝐶𝑂𝑅,𝑡 𝛿1/2 = 𝜔1 + 𝛽1ℎ𝐶𝑂𝑅,𝑡−1 𝛿1/2 + [(1 − 𝛽1𝐿) − (1 − 𝜙1 𝐿) (1 − 𝐿)𝑑1] (|휀𝐶𝑂𝑅,𝑡| − 𝛾1 휀𝐶𝑂𝑅,𝑡)𝛿1 + 𝛽12ℎ𝑃𝐴𝑁,𝑡−1 𝛿2/2 + 𝛽13ℎ𝑈𝑆,𝑡−1 𝛿3/2 + 𝑔1𝐷1 + 𝑔2𝐷2 + 𝑔3𝐷3 + 𝑔4𝐷4 ℎ𝑃𝐴𝑁,𝑡 𝛿2/2 = 𝜔2 + 𝛽2ℎ𝑃𝐴𝑁,𝑡−1 𝛿2/2 + [(1 − 𝛽2𝐿) − (1 − 𝜙2 𝐿) (1 − 𝐿)𝑑2](|휀𝑃𝐴𝑁,𝑡| − 𝛾2 휀𝑃𝐴𝑁,𝑡)𝛿2 + 𝛽21ℎ𝐶𝑂𝑅,𝑡−1 𝛿1/2 + 𝛽23ℎ𝑈𝑆,𝑡−1 𝛿3/2 + 𝑔5𝐷1 + 𝑔6𝐷2 + 𝑔7𝐷3 + 𝑔8𝐷4 ℎ𝑈𝑆,𝑡 𝛿3/2 = 𝜔3 + 𝛽3ℎ𝑈𝑆,𝑡−1 𝛿3/2 + [(1 − 𝛽3𝐿) − (1 − 𝜙3 𝐿) (1 − 𝐿)𝑑3](|휀𝑈𝑆,𝑡| − 𝛾3 휀𝑈𝑆,𝑡)𝛿3 + 𝛽31ℎ𝐶𝑂𝑅,𝑡−1 𝛿1/2 + 𝛽32ℎ𝑃𝐴𝑁,𝑡−1 𝛿2/2 + 𝑔9𝐷1 + 𝑔10𝐷2 + 𝑔11𝐷3 + 𝑔12𝐷4 (22) 3.5.3. Conditional Covariance Equations Under the sense and evolution of DCC-GARCH Model, we set up conditional covariance equations as follows: 𝑞𝑃𝐴𝑁𝐶𝑂𝑅,𝑡 = (1 − 𝛼𝑃𝐴𝑁𝐶𝑂𝑅,𝑡 − 𝛽𝑃𝐴𝑁𝐶𝑂𝑅,𝑡)�̅�𝑃𝐴𝑅𝐶𝑂𝑅 + 𝛼𝑃𝐴𝑁𝐶𝑂𝑅,𝑡𝑢𝑃𝐴𝑁,𝑡−1 + 𝛽𝑃𝐴𝑁𝐶𝑂𝑅,𝑡𝑞𝑃𝐴𝑁𝐶𝑂𝑅,𝑡−1 𝑞𝑃𝐴𝑁𝑈𝑆,𝑡 = (1 − 𝛼𝑃𝐴𝑁𝑈𝑆,𝑡 − 𝛽𝑃𝐴𝑁𝑈𝑆,𝑡)�̅�𝑃𝐴𝑁𝑈𝑆 + 𝛼𝑃𝐴𝑁𝑈𝑆,𝑡𝑢𝑃𝐴𝑁,𝑡−1𝑢𝑈𝑆,𝑡−1 + 𝛽𝑃𝐴𝑁𝑈𝑆,𝑡𝑞𝑃𝐴𝑁𝑈𝑆,𝑡−1 𝑞𝐶𝑂𝑅𝑈𝑆,𝑡 = (1 − 𝛼𝐶𝑂𝑅𝑈𝑆,𝑡 − 𝛽𝐶𝑂𝑅𝑈𝑆,𝑡)�̅�𝐶𝑂𝑅𝑈𝑆 + 𝛼𝐶𝑂𝑅𝑈𝑆,𝑡𝑢𝐶𝑂𝑅,𝑡−1𝑢𝑈𝑆,𝑡−1 + 𝛽𝐶𝑂𝑅𝑈𝑆,𝑡𝑞𝐶𝑂𝑅𝑈𝑆,𝑡−1 𝑞𝑃𝐴𝑁𝑃𝐴𝑁,𝑡 = (1 − 𝛼𝑃𝐴𝑁,𝑡 − 𝛽𝑃𝐴𝑁,𝑡)�̅�𝑃𝐴𝑁 + 𝛼𝑃𝐴𝑁,𝑡𝑢𝑃𝐴𝑁,𝑡−1 2 + 𝛽𝑃𝐴𝑁𝑃𝐴𝑁,𝑡𝑞𝑃𝐴𝑁𝑃𝐴𝑁,𝑡−1 𝑞𝐶𝑂𝑅𝐶𝑂𝑅,𝑡 = (1 − 𝛼𝐶𝑂𝑅,𝑡 − 𝛽𝐶𝑂𝑅,𝑡)�̅�𝐶𝑂𝑅 + 𝛼𝐶𝑂𝑅,𝑡𝑢𝐶𝑂𝑅,𝑡−1 2 + 𝛽𝐶𝑂𝑅𝐶𝑂𝑅,𝑡𝑞𝐶𝑂𝑅𝐶𝑂𝑅,𝑡−1 𝑞𝑈𝑆𝑈𝑆,𝑡 = (1 − 𝛼𝑈𝑆,𝑡 − 𝛽𝑈𝑆,𝑡)�̅�𝑈𝑆 + 𝛼𝑈𝑆,𝑡𝑢𝑈𝑆,𝑡−1 2 + 𝛽𝑈𝑆𝑈𝑆,𝑡𝑞𝑈𝑆𝑈𝑆,𝑡−1 And ℎ𝑃𝐴𝑁𝐶𝑂𝑅,𝑡 = 242 Edelweiss Applied Science and Technology ISSN: 2576-8484 Vol. 9, No. 8: 231-253, 2025 DOI: 10.55214/2576-8484.v9i8.9257 © 2025 by the author; licensee Learning Gate 𝑢𝑡 = [ 𝑢𝑃𝐴𝑁,𝑡 𝑢 𝐶𝑂𝑅,𝑡 𝑢𝑃𝐴𝑁,𝑡 ] 𝑢𝑡~𝑁(0, 𝐻𝑡) 𝐻𝑡 = [ ℎ𝑃𝐴𝑁𝑃𝐴𝑁,𝑡 2 ℎ𝑃𝐴𝑁𝐶𝑂𝑅,𝑡 ℎ𝑃𝐴𝑁𝑈𝑆,𝑡 ℎ𝐶𝑂𝑅𝑃𝐴𝑁,𝑡 ℎ𝐶𝑂𝑅𝐶𝑂𝑅,𝑡 2 ℎ𝐶𝑂𝑅𝑈𝑆,𝑡 ℎ𝑈𝑆𝑃𝐴𝑁,𝑡 ℎ𝑈𝑆𝐶𝑂𝑅,𝑡 ℎ𝑈𝑆𝑈𝑆,𝑡 2 ] 𝑢𝑖𝑗,𝑡 Represent the standardized residuals 𝑢𝑖𝑗,𝑡 = 𝑖𝑗,𝑡 √ℎ𝑖𝑗,𝑡 𝑖 , 𝑗 = Panama, Costa Rica and the US (23) Variables and Parameters can be defined as follow: 3.5.4. Variable Definition ∆𝐶𝑂𝑅𝑡, ∆𝑃𝐴𝑁𝑡 , ∆𝑈𝑆𝑡: The stock index returns of Costa Rica, Panama and the US at time 𝑡, respectively. 휀𝐶𝑂𝑅,𝑡, 휀𝑃𝐴𝑁,𝑡, 휀𝑈𝑆,𝑡: The residual term of the stock index returns of Costa Rica, Panama and the US at time 𝑡 in conditional mean equation. 휀𝐶𝑂𝑅 𝑡−1, 휀𝑃𝐴𝑁 𝑡−1, 휀𝑈𝑆 𝑡−1: The residual term of the stock index returns of Costa Rica, Panama and the US at time 𝑡 − 1. 𝑍𝑡 : The error correction term at time 𝑡. L: Lag or backshift operator ℎ𝐶𝑂𝑅,𝑡 𝛿1/2 , ℎ𝑃𝐴𝑁,𝑡 𝛿2/2 , ℎ𝑈𝑆,𝑡 𝛿3/2 : Represent conditional variance of Costa Rica, Panama and the US stock markets return at time 𝑡, respectively. ℎ𝐶𝑂𝑅,𝑡−1 𝛿1/2 , ℎ𝑃𝐴𝑁,𝑡−1 𝛿2/2 , ℎ𝑈𝑆,𝑡−1 𝛿3/2 : Represent conditional variance of Costa Rica, Panama and the United States stock markets return at time 𝑡 − 1, respectively. ℎ𝑃𝐴𝑁𝐶𝑂𝑅,𝑡 : The conditional covariance of the stock index returns of Panama and Costa Rica at time 𝑡. ℎ𝑃𝐴𝑁𝑈𝑆,𝑡 : The conditional covariance of the stock index returns of Panama and the United States at time 𝑡. ℎ𝐶𝑂𝑅𝑈𝑆,𝑡 : The conditional covariance of the stock index returns of Costa Rica and the United States at time 𝑡. 𝜌𝑃𝐴𝑁𝐶𝑂𝑅,𝑡 : A pair-wise conditional correlation coefficient between Panama and Costa Rica at time 𝑡. 𝜌𝑃𝐴𝑁𝑈𝑆,𝑡 : A pair-wise conditional correlation coefficient between Panama and the United States at time 𝑡. 𝜌𝐶𝑂𝑅𝑈𝑆,𝑡 : A pair-wise conditional correlation coefficient between Costa Rica and the US at time 𝑡. 243 Edelweiss Applied Science and Technology ISSN: 2576-8484 Vol. 9, No. 8: 231-253, 2025 DOI: 10.55214/2576-8484.v9i8.9257 © 2025 by the author; licensee Learning Gate 𝑞𝑃𝐴𝑁𝐶𝑂𝑅,𝑡: The n x n time-varying covariance matrix of 𝑢𝑡 at time 𝑡 for Panama and Costa Rica stock index. 𝑞𝑃𝐴𝑁𝑈𝑆,𝑡: The n x n time-varying covariance matrix of 𝑢𝑡 at time 𝑡 for Panama and the US stock index. 𝑞𝐶𝑂𝑅𝑈𝑆,𝑡: The n x n time-varying covariance matrix of 𝑢𝑡 at time 𝑡 for Costa Rica and the US stock index. 𝑞𝑃𝐴𝑁𝑃𝐴𝑁,𝑡: The time-varying variance of 𝑢𝑡 at time 𝑡 of Panama stock index. 𝑞𝐶𝑂𝑅𝐶𝑂𝑅,𝑡: The time-varying variance of 𝑢𝑡 at time 𝑡 of Costa Rica Stock index. 𝑞𝑈𝑆𝑈𝑆,𝑡: The time-varying variance of 𝑢𝑡 at time 𝑡 of the US stock index. 𝐷1,𝑡: Dummy variable for the subprime mortgage & global financial crisis (GFC), the 1st week of July 2007 ~ the 3rd week of April 2009 𝐷2,𝑡: Dummy variable for the European debt crisis (EDC), the 4th week of April 2009 ~ the 4th week of March 2012. 𝐷3,𝑡: Dummy variable for the most intense US-China trade war (UCT) from the 3rd week of March 2018 ~ the 4th week of December, 2019 𝐷4,𝑡: Dummy variable for the COVID-19 pandemic period (COV) from the 1st week of March 2020 ~ the 4th week of December 2020 3.5.5. Parameter Definition 𝑢1, 𝑢2, 𝑢3: Intercept term to estimate whether these two countries stock index returns have common long-term trend or not. 𝜆1, 𝜆2, 𝜆3: Measuring the adjustment of speed of the stock index of Costa Rica, Panama and US. 𝑎1𝑖: Estimating the spillover effects for Panama’s stock index return. 𝑏1𝑖: Estimating the spillover effects for Costa Rica’s stock index return. 𝑐1𝑖: Estimating the spillover effects for the US stock index return. 𝜔1, 𝜔2, 𝜔3: Intercept term to estimate whether the conditional variances of the stock index market returns have long-term dependencies or not. 𝛽1, 𝛽2, 𝛽3: Estimate the own-mean spillover effects of the stock return of Panama, Costa Rica and the US. 𝜙1, 𝜙2 and 𝜙3: Estimating the ARCH effects of Panama, Costa Rica and the US stock index prices. 𝛽12: Estimating the volatility spillover effect of Costa Rica stock index returns on Panama stock index return. 𝛽13: Estimating the volatility spillover effect of the US stock index returns on Panama stock index return. 𝛽21: Estimating the volatility spillover effect of Panama stock index returns on Costa Rica stock index return. 𝛽23: Estimating the volatility spillover effect of the US stock index returns on Costa Rica stock index return. 𝛾1, 𝛾2, 𝛾3: Measures the asymmetric effects in Costa Rica, Panama and the US stock markets. 𝑑 : Long-Memory coefficients in the conditional mean equations for Costa Rica, Panama and the US. 𝑑1, 𝑑2, 𝑑3: Long-Memory coefficients in the conditional variance equations for Panama, Costa Rica and the US. �̅�𝑃𝐴𝑁𝐶𝑂𝑅: The n x n unconditional correlation matrix of 𝑢𝑡 between Panama and Costa Rica. �̅�𝑃𝐴𝑁𝑈𝑆: The n x n unconditional correlation matrix of 𝑢𝑡 between Panama and the US. �̅�𝐶𝑂𝑅𝑈𝑆: The n x n unconditional correlation matrix of 𝑢𝑡 between Costa Rica and the US. �̅�𝑃𝐴𝑁𝑃𝐴𝑁: The n x n unconditional correlation matrix of 𝑢𝑡 of Panama stock index. 244 Edelweiss Applied Science and Technology ISSN: 2576-8484 Vol. 9, No. 8: 231-253, 2025 DOI: 10.55214/2576-8484.v9i8.9257 © 2025 by the author; licensee Learning Gate �̅�𝐶𝑂𝑅𝐶𝑂𝑅: The n x n unconditional correlation matrix of 𝑢𝑡 of Costa Rica stock index. �̅�𝑈𝑆𝑈𝑆: The n x n unconditional correlation matrix of 𝑢𝑡 of the US stock index. 𝑢𝑖,𝑡−1: The standardized disturbance matrix at period 𝑡 − 1 for Panama, Costa Rica and the US. αPANCOR and βPANCOR: Nonnegative scalar parameters for Panama and Costa Rica satisfying (𝛼 + 𝛽 < 1) in DCC model. αPANUS and βPANUS: Nonnegative scalar parameters for Panama and the US satisfying (𝛼 + 𝛽 < 1) in DCC model. αCORUS and βCORUS: Nonnegative scalar parameters for Costa Rica and the US satisfying (𝛼 + 𝛽 < 1) in DCC model. k1, k5, k9: Measuring the effect of the subprime mortgage and global financial crisis (GFC) in the mean equations for each stock markets. k2, k6, k10: Measuring the effect of the European debt crisis (EDC) in the mean equations for each stock markets. k3, k7, k11: Measuring the effect of the US-China trade war in the mean equations for each stock markets. k4, k8, k12: Measuring the effect of the COVID-19 pandemic in the mean equations for each stock markets. 𝑔1, 𝑔5, 𝑔9: Measuring the effect of the subprime mortgage and global financial crisis (GFC) in the variance equations for each stock markets. 𝑔2, 𝑔6, 𝑔10: Measuring the effect of the European debt crisis (EDC) in the variance equations for each stock markets. 𝑔3, 𝑔7, 𝑔11: Measuring the effect of the US-China trade war (UCT) in the variance equations for each stock markets. 𝑔4, 𝑔8, 𝑔12: Measuring the effect of the COVID-19 pandemic (COV) in the variance equations for each stock markets. 3.6. Empirical Evidences and Discussions 3.6.1. Results and Analyses of Conditional Mean Equations We use the BHHH method to estimate the coefficients. Table 5 shows that the fractional differencing coefficient (d) of FIEC is 0.92439, significant at the 1% level. With d between 0 and 1, it suggests these stock markets exhibit a long memory effect, where past behavior influences current performance. This implies that historical data can predict future returns, and even delayed news continues to affect today's stock prices. The estimated results of mean return own-spillover (Table 5) shows that Costa Rica's stock return is negatively influenced by its third lag and positively by its second and fourth lags. Panama’s stock return is negatively affected by its second and third lags, and positively by its fourth lag. US stock return is positively influenced by its second lag and negatively by its third lag. The US market is more efficient in responding to market information than Costa Rica and Panama, suggesting that these markets are inefficient and rely on past data to predict future returns. Additionally, the empirical results of the mean return cross-spillover effects of Costa Rica, Panama and the US stock market indicate bidirectional(two-way) spillovers between Costa Rica and Panama stock markets, and unidirectional(one-way) spillovers from the US to both. The US stock market plays a crucial role in price discovery across these three markets. 245 Edelweiss Applied Science and Technology ISSN: 2576-8484 Vol. 9, No. 8: 231-253, 2025 DOI: 10.55214/2576-8484.v9i8.9257 © 2025 by the author; licensee Learning Gate Table 5. Estimates the Parameters of the Conditional Mean Equations for Costa Rica, Panama and the US Stock Markets. d = 0.92439*** (t-value = 7.9043) Costa Rica Coeff t-value Panama Coeff t-value US Coeff t-value 𝑢1 0.1924 1.8716 𝑢2 0.2028*** 20.884 𝑢3 0.2626 1.1321 𝜆1 -0.6156*** -4.0842 𝜆2 -0.4150*** -2.9152 𝜆3 -0.3010*** -3.0250 𝑎11 0.5921 1.0855 𝑏11 0.3115 1.0005 𝑐11 -0.7495 -1.2025 𝑎12 0.8824*** 16.4151 𝑏12 -0.5051*** -10.2712 𝑐12 0.1625*** 7.5656 𝑎13 -5.5014*** -20.3651 𝑏13 -0.6421*** -15.1012 𝑐13 -0.8915*** -10.9981 𝑎14 2.2628*** 11.4571 𝑏14 0.0779*** 20.0008 𝑐14 0.5625 1.0001 𝑎21 0.5141*** 10.0011 𝑏21 0.1225*** 14.1144 𝑐21 0.5115 1.0025 𝑎22 -0.6125*** -4.8754 𝑏22 -0.8261*** -29.0041 𝑐22 -0.2225 -1.0005 𝑎23 0.3130*** 5.2154 𝑏23 0.6925*** 13.5591 𝑐23 0.0190 1.5425 𝑎24 -0.6154*** -7.2152 𝑏24 -0.7025*** -15.2827 𝑐24 -0.2614 -0.0421 𝑎31 -0.6867*** -12.2161 𝑏31 -0.3031*** -10.0101 𝑐31 -0.2889 -1.6826 𝑎32 0.8025*** 20.0518 𝑏32 0.6721*** 18.9081 𝑐32 0.1725 1.4826 𝑎33 -0.4118*** -12.0121 𝑏33 -0.0181*** -16.2025 𝑐33 -0.1339 -1.8057 𝑎34 0.1329*** 18.0705 𝑏34 -0.1151*** -21.0051 𝑐34 0.1055 1.2826 𝑘1 -0.2256*** -3.1101 𝑘5 -0.2312*** -3.2115 𝑘9 -0.2569*** -4.0315 𝑘2 -0.2025*** -2.9052 𝑘6 -0.2125*** -2.7005 𝑘10 -0.2320*** -3.0025 𝑘3 -0.1727*** -3.6248 𝑘7 -0.1804*** -3.7748 𝑘11 -0.2167*** -4.6456 𝑘4 -0.1614*** -2.8716 𝑘8 -0.1696*** -2.6389 𝑘12 -0.2006*** -2.9726 Note: ***, ** and * denote rejection of the hypothesis at the 1%, 5% and 10% level, respectively. The error correction term (𝑧𝑡−1) for Costa Rica, Panama and the US stock markets is negative and significant at the 1% level (estimated coefficients are 𝜆1 = −0.6156, 𝜆2 = −0.4150 and 𝜆3 = −0.3010) (Table 5). The US has the lowest λ value, indicating a faster adjustment speed to long-run equilibrium compared to Costa Rica and Panama, showing that the US market leads in returning to equilibrium. This supports the notion that the US stock market plays a leading or dominant role in these three markets. The estimated dummy variables in the conditional mean equation indicate that major global events exerted statistically significant negative effects on stock returns in Costa Rica, Panama, and the United States. During the Global Financial Crisis (GFC) indicated in dummy variable (𝐷1), the impact coefficients were 𝑘1 = −0.2256 for Costa Rica, 𝑘5 = −0.2312 for Panama, and 𝑘9 = −0.2569 for the United States, all significant at the 1% level, indicating that U.S. stock returns were the most adversely affected. Similarly, the European Debt Crisis (EDC) dummy variable (𝐷2) yielded significant negative coefficients: 𝑘2 = −0.2025 (Costa Rica), 𝑘6 = −0.2125 (Panama) and 𝑘10 = −0.2320 (United States). Again, the United States experienced the largest decline in stock returns. The effects of the U.S.–China Trade War (UCT), captured by the 𝐷3 dummy variable, were also negative and statistically significant at the 1% level: 𝑘3 = −0.1727 (Costa Rica), 𝑘7 = −0.1804 (Panama) and 𝑘11 = −0.2167 (United States). Finally, the COVID-19 pandemic (COV) dummy variable showed substantial and statistically significant negative effects on returns, with estimated coefficients of 𝑘4 = −0.1614, 𝑘8 = −0.1696 and𝑘12 = −0.2006 for Costa Rica, Panama and the United States, respectively. Overall, these findings suggest that all four events led to significant reductions in stock returns across the three markets, with the United States consistently exhibiting the most pronounced declines. Notably, financial crisis events, namely the subprime mortgage crisis and the European debt crisis, exerted considerably stronger negative effects on stock performance than non-financial shocks such as the US-China Trade War and the COVID-19 pandemic. This distinction highlights the more disruptive nature of systemic financial disturbances compared to geopolitical or public health-related events [26]. 246 Edelweiss Applied Science and Technology ISSN: 2576-8484 Vol. 9, No. 8: 231-253, 2025 DOI: 10.55214/2576-8484.v9i8.9257 © 2025 by the author; licensee Learning Gate 3.6.2. Results and Analysis of Conditional Variance Equations Table 6 presents the estimated parameters of the conditional variance equations in the FIEC- FIAPGARCH-DCC framework. The subsequent discussions and analysis focuses on the ARCH and GARCH effects, volatility spillover, long memory, and asymmetric effects. Table 6. Estimates Parameters of the Conditional Variance Equations for Costa Rica, Panama and the US Stock Markets. Costa Rica Coeff. t-value Panama Coeff t-value US Coeff. t-value 𝜔1 -0.7721 -1.5150 𝜔2 -0.1921 -1.2051 𝜔3 -0.2125 -1.7123 𝛽1 0.6502*** 3.1848 𝛽2 0.6238*** 4.2455 𝛽3 0.6989*** 4.1142 𝜙1 0.3328*** 3.2628 𝜙2 0.3415*** 3.4125 𝜙3 0.2626*** 4.2628 𝑑1 0.2625*** 3.3754 𝑑2 0.2125*** 3.3614 𝑑3 0.1969*** 3.2536 𝛽12 0.3914*** 3.4415 𝛽21 0.3054*** 3.5458 𝛽31 0.4562 1.1814 𝛽13 0.4518*** 7.9596 𝛽23 0.3868*** 8.2315 𝛽32 0.3233 0.8025 𝛿1 1.3826*** 5.6124 𝛿2 1.5021*** 11.9491 𝛿3 1.6821*** 6.2997 𝛾1 0.2024*** 7.2425 𝛾2 0.2114*** 9.2028 𝛾3 0.2736*** 8.4314 𝑔1 0.1628*** 2.2125 𝑔5 0.6826*** 4.0596 𝑔9 0.5935*** 4.1528 𝑔2 0.1469** 2.0521 𝑔6 0.3544** 2.2021 𝑔10 0.1274** 2.2874 𝑔3 0.1121*** 2.8054 𝑔7 0.3036*** 4.3415 𝑔11 0.2216*** 4.0366 𝑔4 0.1069*** 3.0112 𝑔8 0.2201*** 3.8871 𝑔12 0.1826*** 3.0125 Note: ***, ** and * denote rejection of the hypothesis at the 1%, 5% and 10% level, respectively. As indicated in Table 6, the estimated coefficients of lagged variance (β1 = 0.6502, β2 =0.6238 and β3 = 0.6989) in the conditional variance equations are positive and significant at the 1% level for Costa Rica, Panama and the US. This indicates strong GARCH effects, meaning that current volatility can be predicted by past volatility. Additionally, the coefficients of lagged conditional residuals (𝜙1 = 0.3328, 𝜙2 = 0.3415 𝑎𝑛𝑑 𝜙3 = 0.2626) are also significantly positive at the 1% level, showing that exogenous shocks (unexpected news) significantly cause volatility impacts in all three markets. Regarding inter-market volatility effects, the effects (β12 and β13) of the volatility impacts from Panama and US on Costa Rica stock market volatility are positive and significant at the 5% level (Table 6). Meaning that there exists volatility spillovers measured by ℎ𝑃𝐴𝑁,𝑡−1 𝛿2/2 , ℎ𝑈𝑆,𝑡−1 𝛿3/2 from Panama and US to Costa Rica stock market with US having a greater impact (β13, 0.4518 > β12, 0.3914). The effects (β21and β23) of the volatility impacts from Costa Rica and US on Panama stock market volatility are positive and significant at the 1% level. Meaning that there exists volatility spillovers measured by ℎ𝐶𝑂𝑅,𝑡−1 𝛿1/2 , ℎ𝑈𝑆,𝑡−1 𝛿3/2 from Costa Rica and US to Panama stock market with US having a greater impact (β23, 0.3868 > β21, 0.3054). However, the effects (β21and β23) of the volatility impacts from both Costa Rica and Panama on US stock market volatility are not significant. There is a two-way volatility spillover between Costa Rica and Panama's stock markets, while the US only impacts Costa Rica and Panama through one-way spillovers. International investors should account for both local market volatility and the spillover risks from the US. This might lead investors to use arbitrage strategies or adjust their asset allocation in response to flight-to-quality or flight-to-safety effects. The fractional differencing coefficients (𝑑1, 𝑑2 𝑎𝑛𝑑 𝑑3) measure the long memory effect for each stock market. All coefficients are positive and significant at the 1% level (Table 6), indicating that past information significantly influences future return volatilities. Costa Rica has the highest coefficient (𝑑1=0.2625), suggesting its return volatility takes longer to adjust, followed by Panama (𝑑2=0.2125). The US has the lowest coefficient (𝑑3=0.1969) due to higher market transparency, enabling faster 247 Edelweiss Applied Science and Technology ISSN: 2576-8484 Vol. 9, No. 8: 231-253, 2025 DOI: 10.55214/2576-8484.v9i8.9257 © 2025 by the author; licensee Learning Gate response to new information. Costa Rica and Panama, being less mature and less transparent, exhibit longer-lasting volatility effects. The asymmetric impacts of good and bad news were estimated and are significant at the 1% level for Costa Rica (𝛾1= 0.2024), Panama (𝛾2= 0.2114), and the US (𝛾3= 0.2736) (Table 6). All coefficients are positive, indicating that negative shocks (bad news) have a greater impact on return volatility than positive shocks (good news). The US shows the highest coefficient (𝛾3), reflecting a stronger leverage effect, meaning that the US market is more sensitive to negative news. This is likely due to its higher market dynamism and faster information flow compared to Costa Rica and Panama. The power term coefficient (𝛿) measures variance heterogeneity across stock markets. Table 6 shows that the coefficients for Costa Rica, Panama, and the US are statistically significant at the 1% level. These coefficients are different from 1 and 2, supporting the asymmetric power fractionally integrated model. This suggests that when the series follows a non-normal distribution, power transformations (other than squared terms (𝛿 = 2)) are more appropriate. Research by Ding, et al. [17] and Ding and Granger [27] reinforce that power transformations do not require simple squared shocks in the conditional variance equation. Therefore, the FIAPGARCH model is appropriate for modeling conditional variance of stock market returns. The estimated power term coefficient of the US market (𝛿3=1.6821) is greater than Costa Rica's (𝛿1=1.3826) and Panama's (𝛿2=1.5021), likely due to the trading activities and/or frequencies of Central American (Costa Rica and Panama) stock markets are not higher than the US stock market. Table 6 presents the estimated impacts of the Global Financial Crisis (GFC) and European Debt Crisis (EDC), represented by dummy variables 𝐷1 and 𝐷2, on stock return volatility in Costa Rica, Panama, and the United States stock markets. The coefficients associated with the GFC (𝑔1 = 0.1628, 𝑔5 = 0.6826 and 𝑔9 = 0.5935) and EDC event (𝑔2 = 0.1469, 𝑔6 = 0.3544 and 𝑔10 = 0.1274) are all positive and statistically significant at the 1% and/or 5% significance levels. These results indicate that both financial crises exerted a significant amplifying effect on return volatility across all three markets. Notably, Panama exhibited the highest sensitivity to both financial crisis events, particularly with respect to the GFC. In contrast, the United States displayed greater responsiveness to the GFC than to the EDC. The non-financial shocks, U.S.–China Trade War (UCT) and COVID-19 pandemic (COV), are captured by dummy variables𝐷3 and 𝐷4, respectively. The effects of the UCT event (𝑔3 = 0.1121, 𝑔7 = 0.3036 and 𝑔11 = 0.2216) and COV event (𝑔4 = 0.1069, 𝑔8 = 0.2201 and 𝑔12 = 0.1826) on return volatility are likewise positive and statistically significant at conventional levels. These findings suggest that non-financial events also contributed to heightened return volatility in the three markets, although their impact was less pronounced than that of the financial crises [28]. Panama demonstrates the highest sensitivity to such events, with 𝑔7 and 𝑔8 exceeding the corresponding coefficients for Costa Rica and the United States. The U.S. stock market, meanwhile, shows a greater volatility response to the UCT than to the COVID-19 shock. 3.6.3. Diagnostic Checking for Goodness-of-fit of the Estimated Model To assess model adequacy, we used the Ljung-Box Q test on the estimated standardized residuals (𝑍𝐶𝑂𝑅,𝑡 , 𝑍𝑃𝐴𝑁,𝑡 𝑎𝑛𝑑 𝑍𝑈𝑆,𝑡), the estimated squared residuals(𝑍𝐶𝑂𝑅𝑡 2, 𝑍𝑃𝑁𝑡 2 𝑎𝑛𝑑 𝑍𝑈𝑆𝑡 2), and their cross- products (𝑍𝐶𝑂𝑅,𝑡 𝑍𝑃𝐴𝑁,𝑡 , 𝑍𝐶𝑂𝑅,𝑡 𝑍𝑈𝑆,𝑡 𝑎𝑛𝑑 𝑍𝑃𝐴𝑁,𝑡 𝑍𝑈𝑆,𝑡). The results (Q (12), Q (18), Q (24)) in Table 7 fail to reject the null hypothesis, indicating no autocorrelation or ARCH effects in the residuals. Additionally, tests for the presence of asymmetric behavior of volatility (SBT, NSBT, PSBT and JT) on the estimated standardized residuals show no significant effects. Therefore, these tests confirm that the FIEC-FIAPGARCH-DCC model is appropriate for the three stock markets, and the interpretations of empirical results are valid and reliable. 248 Edelweiss Applied Science and Technology ISSN: 2576-8484 Vol. 9, No. 8: 231-253, 2025 DOI: 10.55214/2576-8484.v9i8.9257 © 2025 by the author; licensee Learning Gate Table 7. Goodness-of-Fit Test and Diagnostic Checking. Costa Rica Panama US 𝑍𝐶𝑂𝑅 = 휀𝐶𝑂𝑅,𝑡/√ℎ𝐶𝑂𝑅,𝑡 𝑍𝑃𝐴𝑁 = 휀𝑃𝐴𝑁,𝑡/√ℎ𝑃𝐴𝑁,𝑡 𝑍𝑈𝑆 = 휀𝑈𝑆,𝑡/√ℎ𝑈𝑆,𝑡 𝑄(12) 21.243 32.331 16.054 𝑄(18) 22.089 33.571 26.714 𝑄(24) 26.178 35.605 34.518 𝑧𝐶𝑂𝑅 2 𝑧𝑃𝐴𝑁 2 𝑧𝑈𝑆 2 𝑄(12) 19.312 30.248 20.369 𝑄(18) 27.010 33.501 30.115 𝑄(24) 30.336 36.771 32.465 𝑍𝐶𝑂𝑅 x 𝑍𝑃𝐴𝑁 𝑍𝑈𝑆 x 𝑍𝐶𝑂𝑅 𝑍𝑈𝑆 x 𝑍𝑃𝐴𝑁 𝑄(12) 27.115 26.551 31.287 𝑄(18) 32.089 31.812 33.456 𝑄(24) 38.323 35.805 38.715 Diagonal Test for Asymmetric Effect of the Estimated Standardized Residuals 𝑍𝐶𝑂𝑅,𝑡/√ℎ𝐶𝑂𝑅,𝑡 𝑍𝑃𝐴𝑁,𝑡/√ℎ𝑃𝐴𝑁,𝑡 𝑍𝑈𝑆,𝑡/√ℎ𝑈𝑆,𝑡 SBT -0.9015 -0.7258 0.3278 NSBT -0.9728 -0.1894 0.5859 PSBT 1.9928 0.6245 0.9498 JT 4.3101 4.2254 2.9134 Note: 𝑍𝑖,𝑡 = 휀𝑖,𝑡/√𝑣𝑎𝑟 (휀𝑖,𝑡) , 𝑍𝑖𝑡 2 and 𝑍𝑖,𝑡 𝑍𝑗,𝑡 represent standardized residuals, squared standardized residuals and cross-product of standardized residuals, respectively. ** and *** denote statistically significant at 5% and 1% level, respectively. 3.7. Results of DCC Estimation and Contagion Effect This section examines the dynamic impacts of conditional correlations in stock market returns for pairs of Costa Rica, Panama, and the US, using the multivariate DCC framework linked to the FIEC- FIAPGARCH model. 3.7.1. Estimated Coefficients of Conditional Correlations In the DCC model, the parameters 𝛼 and 𝛽 quantify the influence of past market behaviors (shocks and correlations) on current relationships between stock markets. Our results show that α + β is close to 1, signifying high correlation between market pairs, suggests that these markets are highly interdependent, reacting to each other’s shocks cross-market shocks. Table 8 shows 𝛼 + 𝛽 = 0.9671 for Costa Rica-Panama, 0.9693 for Costa Rica-US, and 0.9704 for Panama-US, all statistically significant at the 1% level, confirming time-varying correlations. The non-negative values of α and β support the validity of FIEC-FIAPGARCH-DCC model. When α = 0 and β = 0, we get the CCC model [22]. Table 8 summarizes the DCC parameter estimates, showing significant positive values that satisfy 𝛼 + 𝛽 < 1 for all market pairs. The statistical significance of α and β in the DCC model shows strong time-varying co-movement, indicating persistent conditional correlations. The sum of these parameters is close to 1, reflecting high volatility persistence. Since 𝛼 + 𝛽 < 1, the dynamic correlations tend to stabilize around a constant, showing a mean-reverting process. The multivariate FIEC-FIAPARCH-DCC model is essential due to its advantages: capturing long-range dependence, providing pairwise conditional correlations, analyzing behavior during major crises (like subprime mortgage and financial tsunami and European debt crises), and testing for long-memory ARCH effects in these stock prices. 249 Edelweiss Applied Science and Technology ISSN: 2576-8484 Vol. 9, No. 8: 231-253, 2025 DOI: 10.55214/2576-8484.v9i8.9257 © 2025 by the author; licensee Learning Gate Table 8. DCC Parameters Estimates. Costa Rica-Panama Costa Rica-US Panama-US Coeff t-stat Coeff t-stat Coeff t-stat �̂� 0.2130*** 9.9241 0.2105*** 10.0156 0.2114*** 11.4546 �̂� 0.7541*** 26.4578 0.7588*** 25.1316 0.7590*** 26.3987 Persistence 0.9671 0.9693 0.9704 Note: ***, ** and * denote rejection of the hypothesis at the 1%, 5% and 10% level, respectively. Now, the dynamic conditional correlations between Costa Rica-Panama, Costa Rica-US, and Panama-US stock markets are discussed. Table 9 presents average correlation coefficients, considering financial events, with two financial dummies incorporated into the conditional mean and variance equations. Using the ICSS algorithm to detect variance (volatilities) breaks, the data was divided into four periods: chaos and confusion (the 1st week of January 1994 to the 4th week of December 1999), tranquil times (the 1st week of July 2007 to the 3rd week of April 2009), subprime mortgage & global financial crisis (1st week of July 2007 to the 3rd week of April 2009), and the European debt crisis (the 4th week of April 2009 to the 4th week of March 2012). The study examines if conditional correlations increased during these periods compared to those without financial events. The average correlation values for Costa Rica- Panama during these periods are: 0.8146 (chaos and confusion), 0.6501 (tranquil), 0.8810 (GFC), and 0.8525 (EDC). For Costa Rica-US, the averages are: 0.8325 (chaos and confusion), 0.6921 (tranquil), 0.8829 (GFC), and 0.8635 (EDC).For Panama-US, the averages are: 0.8025 (chaos and confusion), 0.6371 (tranquil), 0.9088 (GFC), and 0.9015 (EDC). These results suggest that average correlation values increased during the GFC and EDC periods, indicating contagion effects across these stock markets during these crises. This hypothesis will be further tested using regression analysis of event dummies to detect stock market contagion during these crises. Table 9. Estimated Average Correlation Coefficients during the Periods of Two Events Occurred. Period without considering Subprime Mortgage & Global Financial Crisis or European Debt Crisis Subprime Mortgage & Global Financial Crisis (GFC) European Debt Crisis (EDC) Under Chaos & Confusion Tranquil Time From the 1st week of January 1994 to the 4th week of December 1999 From the 1st week of January 2000 to the 4th week of June 2007 From the 1st week of July 2007 to the 3rd week of April 2009 From the 4th week of April 2009 to the 4th week of March 2012 𝜌𝐶𝑂𝑅𝑃𝐴𝑁 0.8146 0.6501 0.8810 0.8525 𝜌𝐶𝑂𝑅𝑈𝑆 0.8325 0.6921 0.8829 0.8635 𝜌𝑃𝐴𝑁𝑈𝑆 0.8025 0.6371 0.9088 0.9015 Note: DCC equations: 𝜌𝑖𝑗,𝑡 = 𝑞𝑖𝑗,𝑡 √𝑞𝑖𝑖,𝑡𝑞𝑗𝑗,𝑡 . With dummy variables for the global events (GFC & EDC). 3.7.2. Financial Contagion Effects This section analyzes the increased correlation between stock markets after the GFC and EDC to understand how market linkages change during financial crises and detect contagion effects. According to Forbes and Rigobon [29] contagion is defined as a significant rise in cross-market linkages after a shock hits one country. If markets show high co-movement during both stable and crisis periods, it indicates interdependence, not contagion. Here, we apply two dummy variables (D₁ and D₂) in the research period to analyze how the dynamic feature of the correlations change during different crisis phases. The regression model is presented with and without these dummy variables: 250 Edelweiss Applied Science and Technology ISSN: 2576-8484 Vol. 9, No. 8: 231-253, 2025 DOI: 10.55214/2576-8484.v9i8.9257 © 2025 by the author; licensee Learning Gate Excluding dummies: 𝜌𝑖𝑗,𝑡 = 𝜓𝑖𝑗 + 𝛿1𝜌𝑖𝑗,𝑡−1 + 휀𝑖𝑗,𝑡 (24) Including dummies: 𝜌𝑖𝑗,𝑡 = 𝜓𝑖𝑗 + 𝛿1𝜌𝑖𝑗,𝑡−1 + 𝜃1𝐷1,𝑡 + 𝜃2𝐷2,𝑡 + 휀𝑖𝑗,𝑡 (25) In the above auto-regression analysis, we estimate the DCCs (𝜌𝑖𝑗,𝑡) between pairs of stock markets (Costa Rica, Panama, US) using an intercept term (𝜓𝑖𝑗) for each pair of stock markets, two crisis dummies (𝐷1 for GFC, 𝐷2 for EDC) with coefficients 𝜃1and 𝜃2 to capture their effects on correlations. We also include an AR (1) lag (𝜌𝑖𝑗,𝑡−1) with coefficient δ₁ to account for past correlation effects. 휀𝑖𝑗,𝑡 represents the error term with 𝑖𝑖𝑑𝑁(0, σ2). Table 10 compares dynamic conditional correlations under two scenarios. Without the financial crisis dummies, the AR (1) coefficients are 0.8811 for Costa Rica-Panama, 0.8639 for Costa Rica-US, and 0.8296 for Panama-US. These high values indicate strongly persistent autocorrelation, reflecting interactions or interdependence between each pair of stock markets or among these three stock markets. Considering the financial crisis dummies, Table 10 shows the auto-regression results for DCCs (𝜌𝑖𝑗,𝑡) with event dummies (𝐷1 for GFC, 𝐷2 for EDC). The GFC has a significant positive impact on Costa Rica-Panama (𝜃1), Costa Rica-US (𝜃5), and Panama-US (𝜃3) dynamic conditional correlation coefficients, with significance at the 5% and 1% levels. Similarly, the EDC significantly impacts all pairs, Costa Rica-Panama (𝜃2), Costa Rica-US (𝜃4), and Panama-US (𝜃6), at the 5% level. All parameters for the crisis event dummies show a positive impact on dynamic correlation coefficients, indicating that contagion occurred. In addition, the auto-regression results in Table 10 show AR(1) coefficients of 0.8702 for Costa Rica-Panama, 0.8426 for Costa Rica-US, and 0.8025 for Panama-US based on prior-period dynamic conditional correlations. Compared to the case without considering special events, we observe a decrease in these coefficients: from 0.8811 to 0.8702 for Costa Rica-Panama, from 0.8639 to 0.8426 for Costa Rica-US, and from 0.8296 to 0.8025 for Panama-US. This indicates that market interactions are not only driven by co-movement but also by contagion effects from financial events like the GFC and EDC. The changes in correlation are due to external shocks, confirming the existence of contagion. We also find that the GFC had a stronger impact on market correlations than the EDC. For model diagnostics, we still used the BHHH method to estimate the auto-regression coefficients, as shown in Table 10. The results indicate a good fit, with significant R² and F-test statistics for both models (with and without dummy variables). Both the Durbin-h and Ljung-Box Q-tests show no serial correlation in the errors, confirming a white noise process. Therefore, we conclude that our estimated auto-regression models are appropriate, and the interpretations of the above empirical findings are both valid and applicable. 251 Edelweiss Applied Science and Technology ISSN: 2576-8484 Vol. 9, No. 8: 231-253, 2025 DOI: 10.55214/2576-8484.v9i8.9257 © 2025 by the author; licensee Learning Gate Table 10. Auto-regression Estimation for DCC (𝜌𝑖𝑗,𝑡) without and with Two Event Dummies. Note: (1) Auto-regression estimation for DCC 𝜌𝑖𝑗,𝑡 = 𝜓𝑖𝑗 + 𝛿1𝜌𝑖𝑗,𝑡−1 + 휀𝑖𝑗,𝑡 without dummies. (2) Auto-regression estimation for DCC 𝜌𝑖𝑗,𝑡 = 𝜓𝑖𝑗 + 𝛿1𝜌𝑖𝑗,𝑡−1 + 𝜃1𝐷1,𝑡 + 𝜃2𝐷2,𝑡 + 휀𝑖𝑗,𝑡 with dummies. (3) 𝐷1 is the dummy variable for GFC period; 𝐷2 is the dummy variable for the EDC period. (4) Durbin-h = �̂�√ 𝑛 1−𝑛�̂�(�̂�) (5) ***, ** and * denote rejection of the hypothesis at the 1%, 5% and 10% level, respectively. (6) The numbers in parenthesis are the t-statistic values. 4. Concluding Remarks This study examines the interdependence of main Central America (Costa Rica and Panama) and the US stock markets. It uses a dynamic conditional correlation (DCC) model within a multivariate FIEC- FIAPARCH framework, accounting for long memory, power effects, asymmetry (leverage) effects, and time-varying correlations, while considering financial crises like the GFC and EDC. The results show that the FIEC-FIAPARCH-DCC model better captures volatility and time-varying conditional correlations compared to simpler models, with persistent correlations that increase during financial crises. The GFC had a greater impact on cross-market correlations than the EDC. The corresponding coefficient of the error correction term (𝑧𝑡−1) is estimated to be negative and significant, indicating that the markets maintain long-term equilibrium and exhibit co-integration. This suggests that, following an external shock, the Costa Rica, Panama, and US stock markets can return to long-term equilibrium through dynamic adjustments. The US stock market adjusts faster than the Costa Rican and Panamanian markets, meaning it converges more quickly to equilibrium, supporting the notion that the US stock market leads these Central American markets. Thus, the US stock market holds a dominant position among the three stock markets. Additionally, the results show a bidirectional (two-way) mean return spillover effect between Costa Rica and Panama, while the US stock market influences both with a unidirectional (one-way) spillover effect. The US stock market plays a key role for price discovery in these three markets. With regard to inter-market volatility effects, we find a two-way volatility spillover between Costa Rica and Panama stock markets, and a one-way spillover from the US to Costa Rica and Panama. Costa Rica-Panama Costa Rica-US Panama-US Without Dummy With Dummy Without Dummy With Dummy Without Dummy With Dummy 𝜓𝑖𝑗 0.0182*** (3.4159) 0.0121 (1.9685) 0.0084 (1.6578) 0.0075 (0.9967) 0.0502*** (6.8025) 0.0605*** (7.8452) 𝜌𝑖𝑗,𝑡−1(𝛿1) 0.8811*** 27.5141 0.8702*** (61.3054) 0.8639*** (28.5021) 0.8426*** (53.2514) 0.8296*** (28.004) 0.8025*** (45.1146) 𝜃1(𝐷1) 0.0504** (3.0145) 𝜃2(𝐷2) 0.0417** (2.9458) 𝜃3(𝐷1) 0.0881*** (4.3572) 𝜃4(𝐷2) 0.0621** (2.9015) 𝜃5(𝐷1) 0.0521** (3.0012) 𝜃6(𝐷2) 0.0421** (2.0915) 𝑅2 0.6889 0.8025 0.6625 0.7624 0.7012 0.6024 F-Stat 580.4102 1514.8891 541.0012 1192.4151 646.5015 760.3057 MSE 0.1527 0.1428 0.1523 0.1805 0.1559 0.1775 D-h 0.0041 0.0046 0.0041 0.0036 0.0049 0.0029 𝑄(6) 2.6001 2.5415 9.5226 9.5712 7.8326 7.8501 252 Edelweiss Applied Science and Technology ISSN: 2576-8484 Vol. 9, No. 8: 231-253, 2025 DOI: 10.55214/2576-8484.v9i8.9257 © 2025 by the author; licensee Learning Gate International investors should consider not only the volatility in their local markets but also the volatility spillover from the US. This can influence their asset allocation strategies, including arbitrage, flight-to-quality, or flight-to-safety strategies. In terms of long memory, the fractional differencing coefficients suggest that return volatilities for all three markets exhibit long memory, meaning past information can help forecast future volatility. Costa Rica has the highest fractional differencing coefficient, followed by Panama, while the US has the lowest, due to its greater market transparency and faster absorption of new information. Asymmetric effects are present in return volatility, meaning negative shocks have a stronger impact than positive shocks. The three estimated power coefficients (𝛿) are significantly different from unity also significantly different from two, indicating significant differences in the variance for each market. This supports the asymmetric power fractionally integrated model. Finally, Panama’s stock return volatility is more influenced by the EDC event compared to Costa Rica and the US. The US stock market is less affected by the EDC event compared to the GFC event. The results also underscore that Panama's stock market return volatility is the most responsive to both financial and non-financial global shocks. The U.S. market, by comparison, reacts more strongly to the GFC and the UCT, while exhibiting a weaker response to the EDC and the COVID-19 pandemic. Costa Rica, on the other hand, generally exhibits moderate volatility responses across all four events. Moreover, for financial contagion detection, in the DCC analysis with financial structural breaks, we incorporate financial crisis dummies (𝐷1 and 𝐷2) to examine how correlation coefficients (𝜌𝑖𝑗,𝑡) between the paired stock markets (Costa Rica-Panama, Costa Rica-US, and Panama-US) change. Using two event dummies for the GFC and EDC, we analyze the dynamics of correlation changes during these crises and test for contagion effects. The results show that the financial crisis dummies positively impact the conditional correlation coefficients for all stock market pairs, indicating the occurrence of financial contagion. It further indicates that the change in the correlation coefficient is caused by an external shock. This suggests that the changes in market interactions or interrelationships are driven not only by natural co-movement between the markets but also by contagion from external shocks like the GFC and EDC events. Transparency: The author confirms that the manuscript is an honest, accurate, and transparent account of the study; that no vital features of the study have been omitted; and that any discrepancies from the study as planned have been explained. This study followed all ethical practices during writing. Copyright: © 2025 by the author. 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